Wired headsets are commonly used with many portable electronic devices such as portable music players and mobile phones. Headsets can include non-cable components such as a jack, headphones, and/or a microphone and one or more cables that interconnect the non-cable components. Plastic headphones typically include holes that permit the passage of soundwaves from from the inside of the headphones to the outside of the headphones. The creation of these holes can result in remnants left in or around the holes that degrade the aesthetic and acoustic properties of the headphones. Therefore, what are needed are systems and methods for deburring curved plastic objects.